Spectral surgery and high-fidelity quantum state transfer in $XX$ chains

We consider an inhomogeneous $XX$ spin chain which interpolates between the Krawtchouk one with perfect state transfer and the homogeneous $XX$ chain. This model can be used to perform qubit state transfer with sufficiently high fidelity. The advantage of this model with respect to the Krawtchouk chain is that while maintaining high transfer fidelity, the coupling strengths are capped and do not become excessively large as the number of sites grows. The construction is fully analytic and is based on spectral surgery transformations of the homogeneous chain.